Firefighters rescued a seven-month-old boy, who appeared alert on video as he was passed to safety, and later freed one of two older brothers.
Crews are continuing work to release the third boy.
Spokesman Luca Cari said the work to free the boys was complicated, but rescuers were maintaining voice contact with them.
The father told RAI state television that the boys were in their bedroom when the quake struck, while he and his wife were elsewhere in the house.
The mother, who is pregnant, escaped through a window while rescuers reached the father first.
An elderly woman in a church was killed in the quake just before 9pm on Monday, and firefighters said another victim, who appeared to be a woman, had not yet been extracted from under the rubble.
At least 39 more people were injured.
The European Union's humanitarian aid chief offered condolences to those hit by the earthquake and said the 28-nation bloc will provide any support needed.
Commissioner Christos Stylianides said "the EU is fully ready to help" and "we stand ready to provide any immediate assistance the national authorities could require".
That includes use of the EU's emergency satellite mapping system.
Mr Stylianides also commended "the brave first responders working tirelessly on the scene to save lives. They are an example for us all".